The Cooperative Extension Service position is that weed killers and fertilizers should not be mixed. Timing is the main consideration. When weeds need to be killed, most lawn grasses are not actively growing and, therefore, cannot utilize the fertilizer application to its fullest extent. Weeds that are not controlled (and all are not controlled by any one herbicide) are stimulated into phenomenal growth. Also, most fertilizers combined with weeding chemicals are not slow-release formulations. With all of these possible problems and inefficiencies, it is best to keep the weeding separate from the fertilization.
